Abstract
We study vacuum fluctuation properties of an ensemble of S U ( N ) gauge theory configurations, in the limit of many colors, viz. N c → ∞ , and explore the statistical nature of the topological susceptibility by analyzing its critical behavior at a non-zero-vacuum parameter θ and temperature T. We find that the system undergoes a vacuum phase transition at the chiral symmetry restoration temperature as well as at an absolute value of θ . On the other hand, the long-range correlation length solely depends on θ for the theories with critical exponent e = 2 or T = T d + 1 , where T d is the decoherence temperature. Furthermore, it is worth noticing that the unit-critical exponent vacuum configuration corresponds to a non-interacting statistical basis pertaining to a constant mass of η ′ .
Highlights
Quantum chromo-dynamics (QCD) as a Yang–Mills (YM) gauge theory has opened interesting avenues in understanding strong nuclear processes and decay reactions [1,2,3]
By the present intrinsic geometric analysis with free energy F ( x, y) as the real embedding map as in Equation (8), we conclude that a parity odd-bubble hot QCD vacuum configuration generically corresponds to an interacting regular statistical basis over (M2 (R), g) under fluctuations of the system parameters {( x, y) | x, y ∈ M2 (R)}, apart from (i) for a repeated pair of vacuum angles x as given by Equation (29) where the system goes under vacuum phase transitions; and (ii) for the constant temperature line y = d, where d is the decoherence temperature of an arbitrary vacuum system with e 6= 2
As mentioned in the introduction, the state-space geometric characterization has here been investigated for black holes and black branes in various string theory and M-theory vacuum configurations [29,30,31,32,33,34,35,36]
Summary
Quantum chromo-dynamics (QCD) as a Yang–Mills (YM) gauge theory has opened interesting avenues in understanding strong nuclear processes and decay reactions [1,2,3]. In light of our geometric study, important issues pertaining to the statistical stability of parity odd bubbles are determined as an undermining embedding [15] via fluctuation theory analysis [7,8] of free energy and effective potential of a given large N gauge theory configuration [3]. The questions that we attempt to answer in this paper are: (i) under what constraints a considered vacuum ensemble is (un)stable; and (ii) how its parametric vacuum correlation functions scale in terms of the chosen fluctuating parity odd-bubble parameters With such a definite covariant geometric description of a consistent equilibrium statistical system, we can determine a complete set of non-trivial local correlation relations of gauge theory vacuum configurations.
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